Lecture 2

Massey, Ch. 1, Sec. 4

Give examples of compact connected 2-manifolds. Important examples: 2-sphere (which will probably appear in lecture 1), the torus, the projective plane, the Klein bottle.

Some things to perhaps be addressed: What do these look like? (draw pictures) How do we give precise mathematical descriptions (gluing edges: the quotient topology, equations) - how can we use these precise mathematical descriptions to verify that these examples satisfy the definition of a manifold? Which ones are orientable, which ones are not? How the heck do we visualize the projective plane?? Building other examples: discuss the connect sum.